I am currently Arduino users and I was able to communicate with Ublox Neo-6M module successfully with Arduino Uno R3 board using TinyGPS++ Arduino AVR library. Now, my requirements are changed and one of them performance and memory requirements hence I have selected Nucleo L476RG board as it supports Arduino STM32 library.

I was able to successfully testing , Digital I/0, PWM, ADC, DAC, etc., but I could not get Serial2 (PA_2 and PA_3) connecting Ublox module using ArduinoSTM32 libraries.

Also note that Ublox connected via separate 3.3 V power supply with common ground.

I have attached the code for your reference.

Appreciate if you could assist on how to troubleshoot this issue as I am not sure problem with Nucleo board or anything else.

First of all, which core are you using? The Grumpy core or the STM core? This info is important in order to know the corresponding Serial<->USART mappings..
Furthermore, did you check the Nucleo L476RG documentation? Are you aware that PA2 and PA3 are not connected ootb to the CN9 and CN10 connectors and you have to follow the procedure specified in order to connect them?

Moreover, I can see this below from documentation and requires board alteration.
Hence, is there any other way to use any other Serial ports without alteration as breaks ST-Link?

The USART2 interface available on PA2 and PA3 of the STM32 microcontroller can be
connected to ST-LINK MCU, ST morpho connector or to Arduino connector. The choice can
be changed by setting the related solder bridges. By default the USART2 communication
between the target STM32 and ST-LINK MCU is enabled, in order to support virtual COM
port for mbed (SB13 and SB14 ON, SB62 and SB63 OFF). If the communication between
the target STM32 PA2 (D1) or PA3 (D0) and shield or extension board is required, SB62 and
SB63 should be ON, SB13 and SB14 should be OFF. In such case it is possible to connect
another USART to ST-LINK MCU using flying wires between ST morpho connector and
CN3

Please forgive me if I ask silly question as I am very new to STM32 world.